Some Traffic Flow Models Illustrating Interesting Hyperbolic Behavior

This note was prepared for a minisymposium on traffic flow at the SIAM Annual Meeting, July 10, 2001. It contains a brief discussion of two traffic flow models that illustrate some interesting aspects of the theory of nonlinear hyperbolic conservation laws. The first is a model of night-time driving that gives a nonconvex flux function in the classical LWR model, but for which the standard Oleinik entropy condition is not the correct admissibility condition. The second example includes a stiff source term and was designed to illustrate some basic features of detonation waves in a relatively simple context.